自主FDEs的线性稳定性和基本再现数

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-02-24 DOI:10.3934/dcdss.2023082

Xiao-Qiang Zhao

{"title":"自主FDEs的线性稳定性和基本再现数","authors":"Xiao-Qiang Zhao","doi":"10.3934/dcdss.2023082","DOIUrl":null,"url":null,"abstract":"In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory of basic reproduction number $\\mathcal{R}_0$ for general autonomous FDEs. As an illustrative example, we also establish the threshold dynamics for a time-delayed population model of black-legged ticks in terms of $\\mathcal{R}_0$.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The linear stability and basic reproduction numbers for autonomous FDEs\",\"authors\":\"Xiao-Qiang Zhao\",\"doi\":\"10.3934/dcdss.2023082\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory of basic reproduction number $\\\\mathcal{R}_0$ for general autonomous FDEs. As an illustrative example, we also establish the threshold dynamics for a time-delayed population model of black-legged ticks in terms of $\\\\mathcal{R}_0$.\",\"PeriodicalId\":48838,\"journal\":{\"name\":\"Discrete and Continuous Dynamical Systems-Series S\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete and Continuous Dynamical Systems-Series S\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/dcdss.2023082\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Continuous Dynamical Systems-Series S","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/dcdss.2023082","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文首先证明了一类线性自治合作泛函微分方程(FDE)及其关联的无时滞自治合作系统的稳定性等价性。然后给出了一般自治fde的基本再生数$\mathcal{R}_0$的理论。作为一个示例，我们还建立了基于$\mathcal{R}_0$的延时黑腿蜱种群模型的阈值动力学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The linear stability and basic reproduction numbers for autonomous FDEs

In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory of basic reproduction number $\mathcal{R}_0$ for general autonomous FDEs. As an illustrative example, we also establish the threshold dynamics for a time-delayed population model of black-legged ticks in terms of $\mathcal{R}_0$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete and Continuous Dynamical Systems-Series S MATHEMATICS, APPLIED-

CiteScore

3.70

自引率

5.60%

发文量

177

期刊介绍： Series S of Discrete and Continuous Dynamical Systems only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and engineering sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other physical scientists. The journal is published bimonthly.